********* Eigenvalues for the 3+1 transverse lattice ********* Couplings: m^2, G^2 N, beta, la_1, la_2, la_3, la_4, 0 1 2 3 4 5 6 la_5, tau_1, tau_2 (2-9 divided by a^2) 7 8 9 Use chi^2 fit with 40 criteria and tolerance 0.01. Overall scale from fitting lowest state to lattice value. Parity doublets (o,multi,state) with error for difference over average. ( 1, 5,0) and ( 1, 6,0), error 0.25 (-1, 5,0) and (-1, 6,0), error 0.25 ( 1, 7,0) and (-1, 4,0), error 0.25 Spectrum for P_perp a = (0,0), ( 0.25 0) using (# states, multiplet, o, c^2 error for each) = (4, 9 & 8, 1 & -1, 0.25 2 2 2) (4, 8 & 9, 1 & -1, 0.25 2 2 2) (4, 7 & 10, 1 & -1, 0.25 2 2 2) (4, 10 & 7, 1 & -1, 0.25 2 2 2) Spectrum for P_perp a = (0,0), ( 0.25 0.25) using (# states, multiplet, o, c^2 error for each) = (4, 11 & 12, 1 & -1, 0.25 2 2 2) (4, 12 & 11, 1 & -1, 0.25 2 2 2) (4, 14 & 13, 1 & -1, 0.25 2 2 2) (4, 13 & 14, 1 & -1, 0.25 2 2 2). Ordinary spectra multiplets, 4 states, (o,multiplet) = ( 1, 3) (-1, 3) ( 1, 4) (-1, 4) ( 1, 5) (-1, 5) ( 1, 6) (-1, 6) ( 1, 7) (-1, 7) . All spectra extrapolated using (K,p) = (12/2,8) (12/2,6) (14/2,6) (18/2,6) . Winding potential using (n,K,p) = ( 2 0,16/2,6) ( 2 0,16/2,4) ( 2 0,26/2,4) ( 3 0,17/2,7) ( 3 0,17/2,5) ( 3 0,25/2,5) ( 4 0,16/2,8) ( 4 0,16/2,6) ( 4 0,26/2,6) . Roundness of winding using (n,K,p) = ( 2 2,14/2,8) ( 2 2,14/2,6) ( 2 2,22/2,6) with error 1; in G^2 N units. Heavy potential determined using (n,K,p,K_max) = ( 0 0,-26/2,2,3.5) ( 0 0,-26/2,4,3.5) ( 0 0,-26/2,2,3) ( 0 0,-42/2,2,3.5) ( 0 0,-42/2,2,4.25) ( 0 0,-70/2,2,4) ( 0 0,-70/2,2,4.5) , L = 3.577-2.726*m 5.058-3.856*m 7.154-5.452*m (all in G^2 N units); relative scale error=0.1. Roundness determined using (n,K,p,K_max) = ( 1 0,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=1.265-0.964*m and error 0.1; ( 1 0,-13/2,3,3.5) ( 1 0,-13/2,5,3.5) ( 1 0,-13/2,3,3) ( 1 0,-23/2,3,4) ( 1 0,-23/2,3,4.5) ( 1 0,-35/2,3,5) ( 1 0,-35/2,3,6) L=5.058-3.856*m and error 0.1; ( 1 1,-22/2,2,5) ( 1 1,-22/2,4,5) ( 1 1,-22/2,2,4.5) ( 1 1,-44/2,2,5) ( 1 1,-44/2,2,6) ( 1 1,-70/2,2,6) ( 1 1,-70/2,2,7) L=0+0*m and error 0.2; all in G^2 N units. p-extrapolation using n=( 1 0) and (K,p) = (13/2,3) (21/2,3) (45/2,3) (13/2,5) (27/2,5) (13/2,7) (15/2,7) . Result format: Fit info, # steps, chi^2, and p damping, scale G^2 N/sigma. The 10 couplings (G^2 N units); which couplings -- if any -- were fit. Winding potential and heavy souce potential fits. Roundness of winding potential, 1 values, and roundness of heavy source potential, 3 values, (G^2 N units) showing measured value and derived value for each. The rescaled spectrum for each P_perp*a and c^2 values. Finally come the states for the ordinary spectra. 5 100 5444000.51 -0.25 50 0.03249196962 1 0.3587572147 -0.35 -0.02668794163 382.487852 -0.03500887001 185.52576 -1.215874033 15.70843891 2 4 5 6 7 8 9 0.234513 -3.111908 4.075945 0.022028 -0.016440 0.157970 -0.412057 -0.726309 0.521438 0.524000 0.644028 0.531951 0.992886 0.742488 -367.969015 -367.953793 2.855848 -363.054420 -363.609652 -104.167363 -153.555006 -153.470142 15.921360 -111.774049 -111.899174 -23.474707 116.281533 116.460274 33.533528 128.618345 128.832996 40.270838 130.631497 131.247039 115.482196 131.223663 132.575691 253.654720 70.868938 71.056449 35.179060 115.143783 116.313471 219.445778 116.281533 127.252734 2058.313056 126.322307 131.074808 891.619319 -111.774049 -111.720956 9.960763 -88.353694 -88.408960 -10.368457 -5.009374 -0.830129 784.070429 -0.884720 18.196093 3579.761900 -367.969015 -367.939945 2.726883 -153.555006 -153.385628 15.888564 -111.774049 -111.917718 -13.476889 -88.353694 -88.461803 -10.141149 115.143783 115.239820 9.008756 116.281533 116.817791 50.303750 128.618345 128.693990 7.095939 131.223663 131.147530 -7.141721 70.868938 71.240811 34.883702 116.281533 116.169841 -10.477327 126.322307 127.108306 73.730774 128.618345 131.051164 228.211284 -363.054420 -363.946183 -83.652075 -111.774049 -111.946573 -16.183663 -111.635947 -111.773959 -12.946236 -80.000955 -79.959670 3.872800 -367.969015 -153.555006 -75.869973 -54.694186 239.066537 229.552739 282.924282 323.220697 21.390557 190.658999 242.633987 182.654411 70.868938 126.322307 173.788290 164.525007 -363.054420 -80.000955 -111.635947 -77.970932 130.631497 241.925659 258.283337 312.451124 -88.353694 -5.009374 265.645774 140.862919 115.143783 283.972281 189.874099 219.458564 116.281533 131.223663 135.139636 128.618345 -111.774049 -0.884720 22.641006 29.979761 2 36 47939.46015 -0.3836556552 50 0.03249196962 1 0.4354788202 -0.27 -0.02248888343 0.8391888507 0.05931907131 0.1271643309 -1.4345309 0.02970645788 2 4 5 6 7 8 9 0.261602 -1.148628 1.446294 0.023192 0.197181 -0.131718 2.340683 1.124972 0.705126 0.785675 1.126611 0.793773 1.202131 1.032309 -75.862814 -75.843314 4.081038 -74.015900 -74.003861 2.519531 15.693866 16.144208 94.248147 24.051260 23.840483 -44.111539 162.102583 162.171964 14.520167 274.996916 275.132049 28.280912 284.817393 284.945854 26.884475 306.292087 306.226335 -13.760762 162.102583 162.199336 20.248479 199.797391 199.870335 15.265882 274.996916 274.921765 -15.727662 284.817393 284.988494 35.808296 90.784099 90.823021 8.145565 108.659208 108.625799 -6.991779 229.543859 229.604248 12.638313 235.759277 235.783815 5.135373 -75.862814 -75.823894 4.072613 24.051260 24.190999 14.622457 53.976320 53.961494 -1.551455 79.746735 79.856313 11.466329 162.102583 162.254403 15.886548 274.996916 275.040277 4.537338 284.817393 284.949851 13.860508 322.747190 322.702883 -4.636370 162.102583 162.283104 18.889816 199.797391 199.943297 15.267738 274.996916 275.072524 7.911691 284.817393 285.271397 47.507326 -74.015900 -73.991919 2.509400 15.693866 16.032963 35.483287 80.549021 80.559064 1.050848 90.784099 90.780911 -0.333593 -75.862814 24.051260 53.976320 79.746735 367.648040 380.815756 460.864165 551.107507 249.034489 401.197235 456.996968 456.446535 199.797391 299.778733 427.363464 470.780751 -74.015900 15.693866 80.549021 180.080329 306.292087 370.664342 470.408384 492.497197 108.659208 320.002235 411.008828 440.110198 349.168555 427.821696 447.569594 431.602497 162.102583 274.996916 284.817393 322.747190 90.784099 235.759277 229.543859 272.444848 2 11 243.1395245 -0.8399966323 13.87911472 0.03249196962 1 0.5690577892 -0.19 -0.06835478607 50 0.09652390094 12.5 -0.8563551374 -0.8669678471 2 4 5 6 7 8 9 0.242027 -0.923500 0.782443 0.111029 0.200603 -0.182527 2.012993 1.110523 0.630974 0.941936 0.885166 1.077736 1.235441 1.253829 12.670000 12.723811 2.892102 13.588863 13.541171 -2.563276 18.002992 18.060390 3.084868 34.276523 34.287874 0.610107 43.519825 43.546887 1.454473 80.183361 80.229786 2.495141 87.788960 87.838481 2.661591 95.475637 95.450514 -1.350246 43.519825 43.561666 2.248807 57.284321 57.318713 1.848435 80.183361 80.175115 -0.443230 87.788960 87.828605 2.130778 39.109819 39.137849 1.506512 46.100801 46.080824 -1.073693 79.788874 79.806760 0.961276 82.370124 82.395862 1.383327 12.670000 12.653482 -0.443888 18.002992 18.117225 3.069761 34.276523 34.289807 0.356981 39.109819 39.073825 -0.967256 43.519825 43.575584 1.498416 80.183361 80.215828 0.872481 87.788960 87.833250 1.190220 104.726586 104.750814 0.651078 43.519825 43.601905 2.205724 57.284321 57.353125 1.848960 80.183361 80.227050 1.174047 87.788960 87.920065 3.523186 13.588863 13.618134 0.786593 34.326287 34.323861 -0.065183 39.109819 39.112325 0.067343 66.743475 66.783331 1.071043 12.670000 18.002992 34.276523 59.779178 112.332103 114.392004 152.141533 155.191581 89.771739 138.895579 150.455824 147.396625 57.284321 94.792204 131.263597 153.592444 13.588863 34.326287 66.743475 71.889946 95.475637 111.890718 151.498115 156.296178 46.100801 119.859916 133.449232 158.065923 104.726586 139.043687 144.015594 121.676794 43.519825 80.183361 87.788960 107.524472 39.109819 82.370124 79.788874 90.782054 2 11 21.68503708 -1.021564574 9.073597886 0.03249196962 1 0.6376090492 -0.11 -0.1010950241 50 0.1216058558 12.5 -0.8846012892 -0.8326071498 2 4 5 6 7 8 9 0.232515 -0.905522 0.638090 0.113620 0.204710 -0.196982 1.793701 1.034358 0.631115 0.673374 0.892285 0.874873 1.230223 0.875908 12.670000 12.704586 1.167473 19.737491 19.758316 0.702950 20.229984 20.249917 0.672855 28.581584 28.567992 -0.458828 27.561321 27.580580 0.650117 53.649867 53.681794 1.077719 60.197092 60.235924 1.310825 65.962673 65.945844 -0.568090 27.561321 27.593218 1.076698 37.434670 37.462973 0.955382 53.649867 53.649162 -0.023789 60.197092 60.225285 0.951688 30.492090 30.516312 0.817665 35.671515 35.657062 -0.487846 57.590205 57.604315 0.476287 58.454776 58.477374 0.762832 12.670000 12.739198 1.167927 20.229984 20.269325 0.663995 28.581584 28.576844 -0.080014 30.492090 30.454660 -0.631739 27.561321 27.600533 0.661815 53.649867 53.679126 0.493828 60.197092 60.229722 0.550736 70.455136 70.490754 0.601168 27.561321 27.624441 1.065333 37.434670 37.491292 0.955661 53.649867 53.682966 0.558644 60.197092 60.296783 1.682584 19.737491 19.779620 0.711046 28.581971 28.575134 -0.115386 30.492090 30.489789 -0.038828 44.041864 44.069249 0.462206 12.670000 20.229984 28.581584 39.437302 77.141233 77.620596 104.375244 99.575466 65.131780 95.321003 112.971148 104.875419 37.434670 65.734370 82.902788 109.197405 19.737491 28.581971 44.041864 52.097279 65.962673 76.383896 102.251438 104.347675 35.671515 86.407704 93.299797 104.799555 70.455136 95.406993 96.914785 84.532983 27.561321 53.649867 60.197092 76.436700 30.492090 58.454776 57.590205 68.582709 2 18 21.33506012 -1.080549322 8.965054901 0.03249196962 1 0.6937005262 -0.03 -0.1167774583 164.3886888 0.1399141923 57.10859983 -0.8951749637 -0.8002236523 2 4 5 6 7 8 9 0.223568 -0.961690 0.677558 0.117111 0.198611 -0.194209 1.481923 0.911545 0.623177 0.666856 0.888870 0.879082 1.215080 0.868270 12.670000 12.708941 1.248781 24.544103 24.568139 0.770782 25.122905 25.146991 0.772407 32.361842 32.349202 -0.405355 25.905638 25.924041 0.590165 52.382231 52.414081 1.021379 60.399384 60.440487 1.318135 66.339490 66.321110 -0.589434 25.905638 25.940862 1.129569 35.434262 35.467512 1.066269 52.382231 52.380020 -0.070922 60.399384 60.430174 0.987387 32.361842 32.387776 0.831663 37.560657 37.547594 -0.418903 58.768752 58.788358 0.628737 59.968991 59.988942 0.639821 12.670000 12.747901 1.249094 25.122905 25.170680 0.766047 32.361842 32.327205 -0.555390 32.391147 32.377938 -0.211790 25.905638 25.945819 0.644267 52.382231 52.413004 0.493431 60.399384 60.430315 0.495967 68.985293 69.032543 0.757626 25.905638 25.972723 1.075665 35.434262 35.500775 1.066485 52.382231 52.410730 0.456965 60.399384 60.510505 1.781749 24.544103 24.592540 0.776647 32.361842 32.424786 1.009265 32.570325 32.494648 -1.213437 43.713572 43.746987 0.535779 12.670000 25.122905 32.391147 38.800165 77.674237 77.225941 105.606299 100.689642 66.946840 97.030007 108.926561 123.249941 35.434262 65.745698 80.057328 109.958021 24.544103 32.570325 43.713572 53.287199 66.339490 76.521253 100.842038 104.150300 37.560657 88.333394 95.060755 102.593501 68.985293 96.343814 95.421792 87.598662 25.905638 52.382231 60.399384 77.088734 32.361842 58.768752 59.968991 70.547272 2 52 27.38295718 -1.132650713 9.168688387 0.03249196962 1 0.7430043481 0.05 -0.1759678487 1592.776461 0.1852042269 198.6566518 -0.961776276 -0.8554093667 2 4 5 6 7 8 9 0.191600 -1.018933 0.772050 0.115086 0.191930 -0.185789 1.124504 0.610369 0.598293 0.625907 0.850095 0.842829 1.204131 0.812392 12.670000 12.717641 1.339077 24.002207 24.027886 0.721756 24.036695 24.082648 1.291638 33.340855 33.382038 1.157529 24.608766 24.631598 0.641740 51.663273 51.698883 1.000891 59.014676 59.061772 1.323746 66.656523 66.644402 -0.340702 24.608766 24.643351 0.972087 34.282916 34.322227 1.104918 51.663273 51.674667 0.320235 59.014676 59.043051 0.797541 33.340855 33.372999 0.903463 39.449718 39.437995 -0.329518 59.888339 59.912183 0.670194 60.704939 60.726846 0.615770 12.670000 12.765329 1.339735 24.036695 24.116943 1.127790 33.340855 33.253394 -1.229161 36.955241 36.944436 -0.151848 24.608766 24.651042 0.594131 51.663273 51.706115 0.602086 59.014676 59.058150 0.610974 69.268577 69.307797 0.551185 24.608766 24.681372 1.020383 34.282916 34.361548 1.105066 51.663273 51.714308 0.717232 59.014676 59.120706 1.490111 24.002207 24.065148 0.884553 33.340855 33.574451 3.282890 39.855755 39.828825 -0.378463 40.580071 40.371341 -2.933442 12.670000 24.036695 37.283474 36.955241 77.193067 77.389728 106.320455 103.301330 69.191534 101.248720 116.260444 141.204917 34.282916 66.713702 80.848737 113.280740 24.002207 40.580071 39.855755 53.005896 66.656523 76.167793 102.072048 104.515453 39.449718 89.915688 98.751733 107.372394 69.268577 97.386282 98.332559 89.269809 24.608766 51.663273 59.014676 77.667998 33.340855 59.888339 60.704939 70.483462 2 9 536.9319715 -1.283585901 9.025356228 0.03249196962 1 0.7438751173 0.13 -0.1360225496 50 0.1596375224 12.5 -0.96796861 -0.784357302 2 4 5 6 7 8 9 0.205176 -1.075433 0.875652 0.118030 0.191390 -0.189976 1.001811 0.675428 0.600573 0.645912 0.865745 0.865316 1.195675 0.840925 12.670000 12.714308 1.312787 29.300937 29.324541 0.699365 30.169090 30.191431 0.661919 34.778750 36.299445 45.055939 23.641064 23.657858 0.497591 50.776389 50.808189 0.942163 60.587484 60.626609 1.159219 67.090115 67.072645 -0.517604 23.641064 23.677948 1.092807 32.109378 32.148376 1.155467 50.776389 50.772562 -0.113393 60.587484 60.614057 0.787307 34.778750 34.804287 0.756611 39.517707 39.508245 -0.280356 58.247687 58.261086 0.397008 63.666716 63.690009 0.690158 12.670000 12.758637 1.313090 30.169090 30.214298 0.669728 34.778750 34.775725 -0.044813 36.275064 36.325181 0.742450 23.641064 23.681287 0.595878 50.776389 50.807408 0.459515 60.587484 60.608939 0.317844 67.137053 67.203218 0.980181 23.641064 23.708209 0.994705 32.109378 32.187376 1.155484 50.776389 50.801399 0.370499 60.587484 60.696175 1.610168 29.300937 29.347776 0.693894 34.778750 34.824373 0.675871 39.064597 39.048527 -0.238062 40.831477 40.830335 -0.016921 12.670000 30.169090 36.275064 38.656732 78.438686 77.442725 108.131457 106.546499 69.139457 103.808065 120.015859 136.977367 32.109378 65.678858 79.742355 110.548069 29.300937 40.831477 39.064597 55.529573 67.090115 76.942403 99.194330 105.199703 39.517707 87.285059 97.853374 107.783297 67.137053 90.302550 104.910372 88.669829 23.641064 50.776389 60.587484 76.546010 34.778750 58.247687 63.666716 70.377289 2 36 20.50133805 -1.515890939 9.414163582 0.03249196962 1 0.7659264719 0.21 -0.1259036101 118.3531271 0.1735328184 37.47715073 -1.078409389 -0.8005232617 2 4 5 6 7 8 9 0.193714 -1.142611 1.013745 0.110696 0.194067 -0.192988 0.724522 0.533822 0.581660 0.623328 0.840913 0.828040 1.185574 0.809778 12.670000 12.713206 1.260690 33.183347 33.211791 0.829968 33.229183 33.262412 0.969563 36.085229 36.122933 1.100145 23.126924 23.142324 0.449363 51.095597 51.128428 0.957966 61.957476 61.996091 1.126722 69.171209 69.151106 -0.586565 23.126924 23.164614 1.099747 31.014353 31.057770 1.266869 51.095597 51.087398 -0.239219 61.957476 61.982321 0.724934 36.147212 36.171023 0.694760 40.446580 40.438797 -0.227115 58.902153 58.912200 0.293167 66.294970 66.319925 0.728164 12.670000 12.756427 1.260905 33.183347 33.241260 0.844911 36.085229 36.103559 0.267418 36.147212 36.160035 0.187078 23.126924 23.166928 0.583626 51.095597 51.123613 0.408737 61.957476 61.971975 0.211523 67.684495 67.763622 1.154401 23.126924 23.193124 0.965809 31.014353 31.101173 1.266646 51.095597 51.116960 0.311672 61.957476 62.068723 1.623009 33.229183 33.295589 0.968812 36.147212 36.168403 0.309162 40.244888 40.240146 -0.069182 41.358979 41.349445 -0.139089 12.670000 33.183347 36.085229 40.917577 80.553444 79.752814 112.088999 112.343177 71.086066 111.090088 128.546897 138.665590 31.014353 66.846353 81.908686 115.152179 33.229183 40.244888 41.358979 57.707863 69.171209 78.879853 101.242515 108.546869 40.446580 89.100546 97.746114 118.206635 67.684495 90.196139 112.926890 91.162740 23.126924 51.095597 61.957476 78.990217 36.147212 58.902153 66.294970 72.046788 2 10 43.11739652 -1.866217626 8.593664693 0.03249196962 1 0.7318960692 0.29 -0.1065632429 50 0.1539801351 12.5 -1.022404212 -0.7978842732 2 4 5 6 7 8 9 0.194888 -1.136467 1.039743 0.119955 0.187003 -0.190196 0.719996 0.552608 0.577642 0.612357 0.837237 0.847650 1.187598 0.795138 12.670000 12.707430 1.003013 30.976703 30.990260 0.363271 32.081689 32.084518 0.075804 34.406894 34.499140 2.471907 20.756487 20.768357 0.318091 46.836423 46.865232 0.771985 57.341702 57.373086 0.841008 63.840920 63.823610 -0.463846 20.756487 20.788645 0.861737 27.374536 27.411795 0.998429 46.836423 46.826118 -0.276157 57.341702 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70.842839 99.675727 35.556941 30.849541 40.863003 52.968570 59.561543 69.011418 85.319510 94.113842 36.514617 76.764715 80.145703 115.204910 57.711861 79.052209 83.699903 94.472763 18.686669 43.586799 53.746810 67.503947 33.815906 49.322509 59.546040 62.950549